The resulting points of the rectangle after applying rigid transformations are E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1).
How to apply rigid transformations on geometrical loci
Rigid transformations are transformations in which Euclidean distances are conserved in every point of the geometrical locus. Reflections and translations are sound examples of rigid transformations.
Based on all the information given in the statement, we must apply the following vectorial formula to each vertex of the rectangle EFGH:
(x', y') = (x + 3, -y) (1)
If we know that E(x, y) = (-1, 1), F(x, y) = (-1, 3), G(x, y) = (-5, 3) and H(x, y) = (-5, 1), then the new coordinates are calculated below:
E'(x, y) = (2, -1), F(x, y) = (2, -3), G(x, y) = (-2, -3), H(x, y) = (-2, -1)
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